Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Structural Factors Determining the Absorption Spectrum of Channelrhodopsins: A Case Study of the Chimera C1C2

Channelrhodopsins are photosensitive proteins that trigger flagella motion in single-cell algae and have been successfully utilized in optogenetic applications. In optogenetics, light is used to activate neural cells in living organisms, which can be achieved by exploiting the ion channel signaling of channelrhodopsins. Tailoring channelrhodopsins for such applications includes the tuning of the absorption maximum. In order to establish rational design and to obtain a desired spectral shift, a basic understanding of the absorption spectrum is required. We have studied the chimera C1C2 as a representative of this protein family and the first member with an available crystal structure. For this purpose, we sampled the conformations of C1C2 using quantum mechanical/molecular mechanical molecular dynamics and subjected the resulting snapshots of the trajectory to excitation energy calculations using ADC(2) and simplified time-dependent density functional theory. In contrast to previous reports, we found that different hydrogen-bonding networks-involving the retinal protonated Schiff base, the putative counterions E162 and D292, and water molecules-had only a small impact on the absorption spectrum. However, in the case of deprotonated E162, increasing the distance to the Schiff base hydrogen-bonding partner led to a systematic blue shift. The β-ionone ring rotation was identified as another important contributor. Yet the most important factors were found to be the bond length alternation and bond order alternation that were linearly correlated to the absorption maximum by up to 62 and 82%, respectively. We ascribe this novel insight into the structural basis of the absorption spectrum to our enhanced protein setup that includes membrane embedding as well as long and extensive sampling.

Protein Motifs for Proton Transfers That Build the Transmembrane Proton Gradient

Biological membranes are barriers to polar molecules, so membrane embedded proteins control the transfers between cellular compartments. Protein controlled transport moves substrates and activates cellular signaling cascades. In addition, the electrochemical gradient across mitochondrial, bacterial and chloroplast membranes, is a key source of stored cellular energy. This is generated by electron, proton and ion transfers through proteins. The gradient is used to fuel ATP synthesis and to drive active transport. Here the mechanisms by which protons move into the buried active sites of Photosystem II (PSII), bacterial RCs (bRCs) and through the proton pumps, Bacteriorhodopsin (bR), Complex I and Cytochrome c oxidase (CcO), are reviewed. These proteins all use water filled proton transfer paths. The proton pumps, that move protons uphill from low to high concentration compartments, also utilize Proton Loading Sites (PLS), that transiently load and unload protons and gates, which block backflow of protons. PLS and gates should be synchronized so PLS proton affinity is high when the gate opens to the side with few protons and low when the path is open to the high concentration side. Proton transfer paths in the proteins we describe have different design features. Linear paths are seen with a unique entry and exit and a relatively straight path between them. Alternatively, paths can be complex with a tangle of possible routes. Likewise, PLS can be a single residue that changes protonation state or a cluster of residues with multiple charge and tautomer states.

Retinal isomerization and water-pore formation in channelrhodopsin-2

Channelrhodopsin-2 (ChR2) is a light-sensitive ion channel widely used in optogenetics. Photoactivation triggers a trans-to-cis isomerization of a covalently bound retinal. Ensuing conformational changes open a cation-selective channel. We explore the structural dynamics in the early photocycle leading to channel opening by classical (MM) and quantum mechanical (QM) molecular simulations. With QM/MM simulations, we generated a protein-adapted force field for the retinal chromophore, which we validated against absorption spectra. In a 4-µs MM simulation of a dark-adapted ChR2 dimer, water entered the vestibules of the closed channel. Retinal all-trans to 13-cis isomerization, simulated with metadynamics, triggered a major restructuring of the charge cluster forming the channel gate. On a microsecond time scale, water penetrated the gate to form a membrane-spanning preopen pore between helices H1, H2, H3, and H7. This influx of water into an ion-impermeable preopen pore is consistent with time-resolved infrared spectroscopy and electrophysiology experiments. In the retinal 13-cis state, D253 emerged as the proton acceptor of the Schiff base. Upon proton transfer from the Schiff base to D253, modeled by QM/MM simulations, we obtained an early-M/P2390-like intermediate. Rapid rotation of the unprotonated Schiff base toward the cytosolic side effectively prevents its reprotonation from the extracellular side. From MM and QM simulations, we gained detailed insight into the mechanism of ChR2 photoactivation and early events in pore formation. By rearranging the network of charges and hydrogen bonds forming the gate, water emerges as a key player in light-driven ChR2 channel opening.

Active site structure and absorption spectrum of channelrhodopsin-2 wild-type and C128T mutant

We show by extensive ground state and absorption spectra simulations that the channelrhodopsin-2 active site samples three different hydrogen-bonding patterns.

In spite of considerable interest, the active site of channelrhodopsin still lacks a detailed atomistic description, the understanding of which could strongly enhance the development of novel optogenetics tools. We present a computational study combining different state-of-the-art techniques, including hybrid quantum mechanics/molecular mechanics schemes and high-level quantum chemical methods, to properly describe the hydrogen-bonding pattern between the retinal chromophore and its counterions in channelrhodopsin-2 Wild-Type and C128T mutant. Especially, we show by extensive ground state dynamics that the active site, containing a glutamic acid (E123) and a water molecule, is highly dynamic, sampling three different hydrogen-bonding patterns. This results in a broad absorption spectrum that is representative of the different structural motifs found. A comparison with bacteriorhodopsin, characterized by a pentagonal hydrogen-bonded active site structure, elucidates their different absorption properties.

Atomic and molecular analysis highlights the biophysics of unprotonated and protonated retinal in UV and scotopic vision

Unprotonated (UR) and protonated (PR) retinal have marked atomic and molecular differences in cis and trans configurations. In conclusion, UR and PR uphold UV and light vision through their different biophysical properties.

Density functional tight binding: values of semi-empirical methods in an ab initio era

Semi-empirical (SE) methods are derived from Hartree-Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2-3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.

Effect of protein environment within cytochrome P450cam evaluated using a polarizable-embedding QM/MM method

Metalloenzymes accommodate cofactors and substrates in their active sites, thereby exerting powerful catalytic effects. Understanding the key elements of the mechanism via which such binding is accomplished using a number of atoms in a protein is a fundamental challenge. To address this issue computationally, here we used mechanical-embedding (ME), electronic-embedding (EE), and polarizable-embedding (PE) hybrid quantum mechanics and molecular mechanics (QM/MM) methods and performed an energy decomposition analysis (EDA) of the nonbonding protein environmental effect in the "compound I" intermediate state of cytochrome P450cam. The B3LYP and AMBER99/QP302 methods were used to deal with the QM and MM subsystems, respectively, and the nonbonding interaction energy between these subsystems was decomposed into electrostatic, van der Waals, and polarization contributions. The PE-QM/MM calculation was performed using polarizable force fields that were capable of describing induced dipoles within the MM subsystem, which arose in response to the electric field generated by QM electron density, QM nuclei, and MM point charges. The present QM/MM EDA revealed that the electrostatic term constituted the largest stabilizing interaction between the QM and MM subsystems. When proper adjustment was made for the point charges of the MM atoms located at the QM-MM boundary, EE-QM/MM and PE-QM/MM calculations yielded similar QM electron density distributions, indicating that the MM polarization effect does not have a significant influence on the extent of QM polarization in this particular enzyme system.